QUADRATIC TRIGONOMETRIC B-SPLINE GALERKIN METHODS FOR THE REGULARIZED LONG WAVE EQUATION

Dursun Irk; Pınar Keskin

doi:10.11948/2017038

2017 Volume 7 Issue 2

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Dursun Irk, Pınar Keskin. QUADRATIC TRIGONOMETRIC B-SPLINE GALERKIN METHODS FOR THE REGULARIZED LONG WAVE EQUATION[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 617-631. doi: 10.11948/2017038

Citation:

Dursun Irk, Pınar Keskin. QUADRATIC TRIGONOMETRIC B-SPLINE GALERKIN METHODS FOR THE REGULARIZED LONG WAVE EQUATION[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 617-631. doi: 10.11948/2017038

QUADRATIC TRIGONOMETRIC B-SPLINE GALERKIN METHODS FOR THE REGULARIZED LONG WAVE EQUATION

Dursun Irk¹,
Pınar Keskin²

1 Eskişehir Osmangazi University, Department of Mathematics-Computer, 26480, Eskişehir, Turkey;
2 Eskişehir Osmangazi University, Graduate School of Sciences, 26480, Eskişehir, Turkey

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Abstract

Abstract

In this study, a numerical solution of the Regularized Long Wave (RLW) equation is obtained using Galerkin finite element method, based on two and three steps Adams Moulton method for the time integration and quadratic trigonometric B-spline functions for the space integration. After two different linearization techniques are applied, the proposed algorithms are tested on the problems of propagation of a solitary wave and interaction of two solitary waves. For the first test problem, the rate of convergence and the running time of the proposed algorithms are computed and the error norm L∞ is used to measure the differences between exact and numerical solutions. The three conservation quantities of the motion are calculated to determine the conservation properties of the proposed algorithms for both of the test problems.
- Finite element method /
- spline approximation /
- solitary waves equation
MSC: 65M60;41A15;74J35

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References

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